The class equation for a group G can be written |G| = |Z(G)| + 2|CI(a;)|, where the sum runs over representatives of the distinct non-central conjugacy classes. %3D Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}. Therefore the class equation of S3 is given by | S3 = 1+2+3. p9:30 #2 a) Find the conjugacy classes for D3 and write the class equation for Dg. b) Explain why each of the following could not be the class equation of a group G. i) G| = 3 + 3 +3 ii) G| = 2+3 + 3+7 ii) |G| = 1+3 +6+8 attino low 2.
The class equation for a group G can be written |G| = |Z(G)| + 2|CI(a;)|, where the sum runs over representatives of the distinct non-central conjugacy classes. %3D Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}. Therefore the class equation of S3 is given by | S3 = 1+2+3. p9:30 #2 a) Find the conjugacy classes for D3 and write the class equation for Dg. b) Explain why each of the following could not be the class equation of a group G. i) G| = 3 + 3 +3 ii) G| = 2+3 + 3+7 ii) |G| = 1+3 +6+8 attino low 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The class equation for a group G can be written |G| = |Z(G)| + 2|CI(a;)|, where the
sum runs over representatives of the distinct non-central conjugacy classes.
%3D
Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}.
Therefore the class equation of S3 is given by | S3 = 1+2+3.
p9:30
#2 a)
Find the conjugacy classes for D3 and write the class equation for Dg.
b)
Explain why each of the following could not be the class equation of a group G.
i)
G| = 3 + 3 +3
ii)
G| = 2+3 + 3+7
ii)
|G| = 1+3 +6+8
attino
low
2.
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